We prove the results on the tangent spaces to Schubert varieties announced in w ลฝ . x V. Lakshmibai, Math. Res. Lett. 2 1995 , 473แ477 for G classical. We give two descriptions of the tangent space to a Schubert variety at id. The first description is in terms of the root system, and the second one
Permutation representations on Schubert varieties
โ Scribed by Julianna S. Tymoczko,
- Book ID
- 118225197
- Publisher
- John Hopkins University Press
- Year
- 2008
- Tongue
- English
- Weight
- 498 KB
- Volume
- 130
- Category
- Article
- ISSN
- 0002-9327
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๐ SIMILAR VOLUMES
We give an elementary proof of the following known fact: any multihomogenous component in the homogeneous coordinate ring of a Schubert variety inside ลฝ GL rB has basis given by the standard monomials V. Lakshmibai et al., 1986, J. n . Algebra 100, 462แ557 .
We prove results on the tangent spaces to Schubert varieties in G/B for G classical. We give a description of the tangent space to a Schubert variety X w at a T -fixed point e ฯ in terms of the root system. We also relate this result to multiplicities of certain weights in the fundamental representa